The number of foreign fighters flowing into Syria is growing as the civil war stretches into its third year, raising concern that insurgents trained by al-Qaeda-linked groups will spread their ideology and return to their native countries determined to mount attacks on Western targets, senior U.S. intelligence officials said Wednesday.

The officials said that thousands of fighters have entered Syria to join an insurgency that is increasingly dominated by groups with militant Islamist agendas. Most of those fighters have arrived from the Middle East and North Africa, officials said, but as many as 700 have traveled from Europe and are believed to carry Western passports.

At the same time, dozens of Americans have either entered Syria to take part in the civil war, or sought to do so but were arrested in the United States or otherwise prevented from fulfilling their plans, the officials said.

They characterized Syria as the most significant magnet for Islamist militants since the war in Iraq a decade ago.

“It is the biggest draw,” one senior U.S. intelligence official said. Analysts at the National Counterterrorism Center, the CIA and other U.S. intelligence agencies assess that the streams of fighters entering Syria are likely to continue to expand. Neither the insurgent groups nor forces loyal to Syrian President Bashar al-Assad appear poised to gain control of the conflict, the official said, meaning “we could see this dragging on for a very long time.”

During a briefing with reporters, the officials described developments in Syria on the condition that they not be identified by name.

The surging number of fighters flocking to Syria has given rise to new insurgent factions that U.S. officials referred to as “migrant brigades,” groups comprising militants with similar backgrounds and nationalities.

One of the largest of the new groups, Jaysh al-Muhajireen Wal Ansar, formed in March and is made up mainly of fighters from central Asia and European countries, officials said.

The brigades are willing to “accept fighters without the bona fides” to join Jabhat al-Nusra and other insurgent groups that are more closely aligned with al-Qaeda and wary of volunteers from Western countries perceived as potential plants by foreign intelligence services, a second U.S. intelligence official said.

The U.S. officials said they were unaware of any case so far in which a fighter in Syria had returned to his home country to carry out a terrorist attack. Still, the officials said that the Syrian civil war could serve as a catalyst for future terrorist cells and threats much the way Afghanistan did in the 1980s.

“Those who go to Syria gain battlefield experience, indoctrination if they don’t already have it,” and form connections with like-minded Islamist militants that are likely to last after the civil war ends, the senior U.S. intelligence official said.

The officials noted the insurgent groups’ sophisticated use of social media services including Twitter and videos on YouTube to recruit fighters from abroad, with messages drafted in languages including English and French.

The officials said they have not seen any recruiting effort so far aimed specificially at Americans, and noted that fighters from the United States represent a tiny fraction of the opposition in Syria, in part because of the distance between the two countries.

There have been several arrests in the United States of individuals accused of seeking to travel to Syria to fight alongside militant groups linked to al-Qaeda. A U.S. Army veteran, Eric Harroun of Phoenix, was arrested in March and charged with fighting alongside a Syrian rebel group before pleading guilty to a lesser count.

A much smaller number of foreign fighters, mostly Shiite militants with ties to Iran or Hezbollah, have entered Syria to fight in support of Assad, officials said.

The U.S. officials said that their estimates of the number of foreign fighters, as well as the percentages coming from Western nations, are imprecise because of difficulties in obtaining reliable data and intelligence. European officials have estimated that 800 to 900 militants had traveled to Syria, mostly from Britain, France, the Netherlands, Belgium and Germany.